If two lines coincide at infinitely many points, then the pair of linear equations representing these lines will have ______.

A pair of linear equations which has coincident lines have infinitely many distinct solutions. 

For example,

If the two linear equations are of the form:

${\mathrm{a}}_1\mathrm{x}+{\mathrm{b}}_1\mathrm{x}+{\mathrm{c}}_1=0$

${\mathrm{a}}_2\mathrm{x}+{\mathrm{b}}_2\mathrm{x}+{\mathrm{c}}_2=0$

Then the system of equation will have infinitely many solutions if:

$\frac{{\mathrm{a}}_1}{{\mathrm{a}}_2}=\frac{{\mathrm{b}}_1}{{\mathrm{b}}_2}=\frac{{\mathrm{c}}_1}{{\mathrm{c}}_2}$ .

Such equations would result in coincident lines when plotted on a graph.